ECON 301
Spring 2019
03/04/2019
Midterm Exam
Time Limit: 110 Minutes
Name-Surname:
Student ID:
Instructions
• Students should follow the instructions of the examiner. Firm action will be taken against
students committing academic fraud.
• Enter all requested information on the top of this page.
• Organize your work, in a reasonably neat and coherent way, in the space provided.
• If you need more space, use the back of the pages; clearly indicate when you have done this.
• This exam contains 10 pages (including this cover page). Check to see if any pages are missing.
• In parentheses, each question states the number of points out of 100 that can be earned by
answering it correctly.
• Provide precise and complete answers. Do not include irrelevant information.
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1. Impact of Lead water pipes on infant mortality
Lead is toxic, particularly for young children, and for this reason government regulations
severely restrict the amount of lead in our environment. But this was not always the case.
In the early part of the 20th century, the underground water pipes in many U.S. cities contained lead, and lead from these pipes leached into drinking water. In this exercise you will
investigate the effect of these lead water pipes on infant mortality. The data set contains data
on infant mortality, type of water pipes (lead or non-lead) and water acidity (pH). The descriptions of the variables in the data set are below
Stata summarizes the key variables as follows:
Following table shows the correlation between these variables:
You decide to study the effect of lead water pipes on infant mortality using a linear regression
of infrate on lead and ph.
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(a) (10 points) What is the zero conditional mean assumption in the following estimated
model? Discuss whether this assumption holds here (you can benefit from the above
correlation matrix). Explain why this assumption is important for measuring the causal
(ceteris paribus) effect of use of Lead water pipes on infant mortality.
(b) (5 points) Based on the regression results in question (a), what is the difference in infant
mortality rates in cities with lead water pipes and cities with non-lead water pipes? Is the
difference statistically significant at 10% significance level? Explain.
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(c) (10 points) What would you expect about the magnitude (absolute value) of the estimate
of the slope parameter on lead when we additionally include the variable ph in the regression model? (Is there going to be an increase or decrease in the magnitude of the
coefficient?) Explain your answer based on the correlation matrix provided above.
(d) (10 points) Next, we run a regression of infrate on lead and ph. Interpret the signs
and magnitudes of the estimated coefficients (for lead and ph) in the following regression
output? Are these coefficient estimates statistically significant at 1% significance level
(explain)?
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(e) (10 points) The amount of lead leached from lead pipes depends on the chemistry of the
water running through the pipes. The more acidic the water (that is, the lower its pH),
the more lead is leached. Therefore, we run a regression of infrate on lead , ph, and the
interaction term lead ph. Interpret the sign of the coefficient of lead ph in the following
regression output?
(f) (5 points) Interpret the value of the R-squared for the regression model in question (e).
Is its value evidence for or against a causal interpretation of the estimated effect of lead
on infrate?
(g) (5 points) Interpret the estimated parameter cons in the reported results in question (e)?
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2. Testing ”More Guns Less Crime” Hypothesis
Some U.S. states have enacted laws that allow citizens to carry concealed weapons. These laws
are known as ”shall-issue” laws because they instruct local authorities to issue a concealed
weapons permit to all applicants who are citizens, are mentally competent, and have not been
convicted of a felony. (Some states have some additional restrictions.) Proponents argue that
if more people carry concealed weapons, crime will decline because criminals will be deterred
from attacking other people. Opponents argue that crime will increase because of accidental or
spontaneous use of the weapons. In this exercise, we analyze the effect of concealed weapons
laws on violent crimes. The data set contains data from the 50 U.S. states plus the District of
Columbia for the years 1977 through 1999. The descriptions of the variables in the data set
are below
Stata summarizes the key variables as follows:
You decide to study the effect of ”shall-issue” laws on violent crime rates using a linear regression
of lnvio (Log of vio) on shall and other control variables (we included average income in
logarithmic form (log of avginc))
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(a) (15 points) Below is the regression results. Interpret the sign and magnitude of the coefficient of shall in the following regression output? Interpret the sign and magnitude of the
coefficient of lnavginc? Interpret the sign and magnitude of the coefficient of density?
(b) (10 points) Endogeneity problem: Discuss whether the estimated coefficient for shall can
be considered as the causal effect. Provide an argument why we might be estimating a
negative effect of shall on violent crime rate although it is not true?
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(c) (5 points) Based on the following figure showing the two-way scatterplot for population
and violent crime, discuss how would you include ”population (pop)” in the above model
(Level? Log? or Quadratic?) Explain your answer.
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(d) (5 points) Based on the following estimation results and the results in question (a), which
model would you prefer (including population variable as it is (as in question a), in
quadratic form (first estimation below) or in logarithmic form (second estimation below))? Explain your answer.
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(e) (10 points) Below is the variance formula of OLS estimator for βj :
V ar(β̂j ) =
σ2
SSTj (1 − Rj2 )
Based on this formula, discuss how the following cases will affect the standard error of the
estimated coefficient, βbj .
i) an increase in the sample size
ii) adding control variables hat are highly correlated with xj
iii) adding control variables that are not correlated with xj